The Cobblers have emerged as the most likely challengers to Rob Edwards' high-flyers, but they are still four points adrift of the leaders having played a game more.
A run of 25 points gleaned from a possible 30 has seen Town make second place their own, with a five-point gap having opened up to fourth place.
But that impressive run has seen them make little impression on Forest Green's advantage as they have pieced together a nine-match unbeaten run of their own, winning six of those.
The Cobblers have been denied the opportunity to stretch their own winning streak to four matches as Saturday's clash with Barrow was postponed due to a Covid outbreak in the Town camp, and the Boxing Day showdown with Walsall has already gone by the wayside.
There has to be serious doubts over the scheduled trip to Scunthorpe United next Wednesday (Dec 29) as well, but whenever Town do get back out on the field, Brady will be focusing on maintaining the gap between Town and those below them - and closing in on the top spot.
Asked about the opening of the big advantage to fourth place, the Town boss said: "Winning eight games out of 10 has really helped that.
"It is really good consistency in anybody's book, and with that you are either going to climb the table or pull away if you are up there in the table.
"We are up there, and we want to now try to look up and not down.
"As long as we can keep looking up and clawing our way, inch by inch, closer to Forest Green then that is what we want to do."
The Cobblers have reached their lofty position with a run of hard-fought victories, seeing off Oldham, Leyton Orient, Exeter City and Harrogate Town by a single goal margin.
They are second in the table without having really hit their best form, but they have developed a knack for scoring goals when it matters, and that is a habit Brady is hoping his players can gold on to.
"It is a good thing to have in a side to find a goal at the right time, that really knocks the wind out of the opposition," said the Australian.
"That has been important and really helped us in the past week or so.
"You can't ask for better than that, especially when you are in tight situations and you might be under the cosh a little bit.
"But to find a way and come out the other side has been really pleasing."